Topoi 3 (1):13-22 (1984)

Abstract
The purpose of this paper is to justify the claim that Topos theory and Logic (the latter interpreted in a wide enough sense to include Model theory and Set theory) may interact to the advantage of both fields. Once the necessity of utilizing toposes (other than the topos of Sets) becomes apparent, workers in Topos theory try to make this task as easy as possible by employing a variety of methods which, in the last instance, find their justification in metatheorems from Logic. Some concrete instances of this assertion will be given in the form of simple proofs that certain theorems of Algebra hold in any (Grothendieck) topos, in order to illustrate the various techniques that are used. In the other direction, Topos theory can also be a useful tool in Logic. Examples of this are independence proofs in (classical as well as intuitionistic) Set theory, as well as transfer methods in the presence of a sheaf representation theorem, the latter applied, in particular, to model theoretic properties of certain theories.
Keywords Topos Theory  Logic  Model Theory  Set Theory
Categories (categorize this paper)
DOI 10.1007/BF00136116
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,634
Through your library

References found in this work BETA

Sheaves and Logic.M. P. Fourman, D. S. Scott & C. J. Mulvey - 1983 - Journal of Symbolic Logic 48 (4):1201-1203.
La Logique Des Topos.André Boileau & André Joyal - 1981 - Journal of Symbolic Logic 46 (1):6-16.
Doctrines in Categorical Logic.Anders Kock & Gonzalo E. Reyes - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 90.

View all 7 references / Add more references

Citations of this work BETA

Category Theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.

Add more citations

Similar books and articles

Topological Completeness for Higher-Order Logic.S. Awodey & C. Butz - 2000 - Journal of Symbolic Logic 65 (3):1168-1182.
The Skolem-Löwenheim Theorem in Toposes.Marek Zawadowski - 1983 - Studia Logica 42 (4):461 - 475.
The Uses and Abuses of the History of Topos Theory.Colin Mclarty - 1990 - British Journal for the Philosophy of Science 41 (3):351-375.
What is Categorical Structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 151--161.

Analytics

Added to PP index
2009-01-28

Total views
100 ( #94,582 of 2,348,973 )

Recent downloads (6 months)
4 ( #186,326 of 2,348,973 )

How can I increase my downloads?

Downloads

My notes